An evaluation of path integrals by a Fourier sine series of the form Eq. (REF ) is a frequently used approach. (See e. g. Ref.[1]}) However, this method fails (as shown below) when magnetic fields are present.
This fact stands in contrast to an evaluation by the complex Fourier series Eq. (REF ) where one can calculate the corresponding path integral correctly provided that one \(\zeta \) -regularizes the integral appropriately.
